The “fuzzball proposal” suggests that “microstate geometries” provide a classical, microscopic description of black holes. These spacetimes are similar to black holes at large distances, however, they lack a horizon or black hole region.

Recent numerical and heuristic work indicates that microstate geometries might be classically unstable, and this is now supported by several rigorous results. Overall, these results show that linear fields on microstate geometries behave very strangely indeed: despite the presence of an ergoregion, they avoid the “Friedman instability” and no exponentially growing modes are present. On the other hand, linear fields decay extremely slowly – even slower than can be achieved by any possible arrangement of mirrors in Minkowski space! Additionally, the presence of an “evanescent ergoregion” can lead to an arbitrarily large amplification of the local energy, despite the presence of a globally causal Killing vector field and the lack of any growing modes. Taken together, these results indicate a very unusual kind of instability for microstate geometries.

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